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'''Geometry''' is the branch of mathematics that deals with properties of [[shape]]s and spatial relationships. It is one of the five most basic branches of [[pure mathematics]], the others being [[algebra]], [[number theory]], [[analysis]], and [[logic]]. Primarily, the subject may be divided into six branches:

'''Geometry''' is the branch of [[mathematics]] that deals with properties of [[shape]]s and spatial relationships. It is one of the five most basic branches of [[pure mathematics]], the others being [[algebra]], [[number theory]], [[analysis]], and [[logic]]. Primarily, the subject may be divided into six branches:

* [[Euclidean geometry]] studies geometry where the [[parallel postulate]] is valid.

* [[Euclidean geometry]] studies geometry where the [[parallel postulate]] is valid. This includes [[plane geometry]].

* [[Non-Euclidean geometry]] studies geometry where the parallel postulate is false.

* [[Non-Euclidean geometry]] studies geometry where the parallel postulate is false.

* [[Differential geometry]] studies properties of smooth shapes called differentiable [[manifolds]] by analyzing their [[curvature]] properties.

* [[Differential geometry]] studies properties of smooth shapes called differentiable [[manifolds]] by analyzing their [[curvature]] properties.

* [[Algebraic geometry]] studies properties of shapes defined by [[algebraic]] [[equation]]s, by making use of the additional structures these objects inherit from their algebraic nature.

* [[Algebraic geometry]] studies properties of shapes defined by [[algebraic]] [[equation]]s (e.g. a [[parabola]]) by making use of the additional structures these objects inherit from their algebraic nature.

* [[Topology]], broadly speaking, studies properties of shapes invariant under [[continuous function]]s.  

* [[Topology]], broadly speaking, studies properties of shapes invariant under [[continuous function]]s.  

* [[Geometric measure theory]] studies objects that possess a notion of fractional dimension, such as fractals.

* [[Geometric measure theory]] studies objects that possess a notion of fractional dimension, such as [[fractal]]s.

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